Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Linear Algebra Linear Dependence, Basis & Dimension
Let x = (x1, x2, x3), y = (y1, y2, y3) ℝ3 be linearly independent. Let δ1 = x2y3 - y2x3, δ2 = x1y3 - y1x3, δ3 = x1y2 - y1x2. If V is the span of x, y then
1
V = {(u, v, w) : δ1u - δ2v + δ3w = 0}
2
V = {(u, v, w) : -δ1u + δ2v + δ3w = 0}
3
V = {(u, v, w) : δ1u + δ2v - δ3w = 0}
4
V = {(u, v, w) : δ1u + δ2v + δ3w = 0}